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Can We Measure the Higgs Boson's Quantum Numbers?

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Can We Measure the Higgs Boson's Quantum Numbers? Can we measure the Higgs boson’s quantum numbers? D.J. Miller University of Glasgow 22 nd November 2007 Outline: Introduction The Higgs boson’s Spin The Higgs boson’s CP CP Violating Higgs bosons Conclusions Are secrets of the universe just about to be revealed? The invisible force which explains the nature of life, the universe and everything was first predicted by an Edinburgh scientist. Now, a team of Glasgow University physicists are preparing to discover if he was right. "The exciting thing is that we have no idea what we will find," say Parkes. " It could be the Higgs boson, or it could be something else entirely.” At dinner parties, Dr Parkes is often too embarrassed to admit what he does for a living. There is even a plucky band of space boffins … [led] by an English ex-pop star. You couldn’t make it up. Physicist Brian Cox, an expert on the forces created by the Big Bang and science adviser on Sunshine, played keyboards for Nineties rock group D:Ream. Almost right! (missed gW) This is just a tiny part of an equation which stretches to 36 lines. Scientists say it explains everything in the universe. The only trouble is that one of its key ingredients, the Higgs particle represented by the letter H, has never been found. CERN hope their particle machine will find the missing clue. Brian says: “It explains everything in physics from why is the sky blue to why chemistry works.” They are just one of the things Brian and his colleagues hope to find in a £2BILLION project to blast, pulverise and smash the atom in a recreation of the forces unleashed by the Big Bang…. 1. Introduction (or Tevatron) If the Higgs boson exists, it is almost certain that the LHC will see it within 10fb -1 or so: Notice that heavier Higgs bosons are dominated by leptons. I have a question for the experimenters about CMS’s figures (I know this is the wrong audience….) CMS Also produce a “required luminosity” plot: How can we reconcile these plots? This reflects the Higgs decay branching ratios: For low Higgs mass, the Higgs predominantly decays to b-quarks For higher Higgs mass, the Higgs predominantly decays to gauge bosons. The leptons is more significant than because it is so clean. We have good indications that the Higgs boson will be reasonably light: triviality vacuum stability Electroweak precision data: (95% conf.) Folding in LEP limit gives (95% conf.) [Numbers from Terry Wyatt’s talk at EPS 07] Imagine we discover a “Higgs-like” resonance at the LHC. How do we know that it is the Higgs boson? We need to measure: Higgs CP and spin The Higgs is a pretty weird object – we have never seen a fundamental scalar before. Also should ensure it is not a pseudoscalar, or a mixture of scalar and pseudoscalar. Higgs couplings to fermions and gauge bosons Must be proportional to the particle masses Higgs self couplings In principle allows us to reconstruct the Higgs potential (out of reach of the LHC) The first 2 are intimately linked since CP and spin restrict the form of the couplings. In this talk, I will concentrate on the first requirement: Higgs CP and spin I consider a reasonably heavy Higgs boson, 150 - 200 GeV, and look at its decay All the information on the Higgs spin Z and CP is contained in this vertex H Z Our approach: Write down the most general vertex for a particle of a particular spin and CP coupling to ZZ and see how it differs from the SM Higgs. In principle, there are lot of other production mechanisms, decays and couplings one could exploit. For example, Production at LHC: (W boson fusion) Production at ILC: Decays: [see arXiv:0708.0458 for references] 2. Higgs boson spin (or lack thereof) Let’s start with an example: distinguishing the SM state from an axial vector SM coupling: General axial-vector coupling: “constants” could be Z momenta: (dimensionless) functions of momenta Notice that the 0 - terms always contain a momentum dependence, unlike the SM. Examine the dependence of the cross-section on the virtuality of the off-shell Z boson: β is the Z*/Z three-momentum in the H rest frame, in units of the Higgs mass M H. This β comes from phase space , not the Higgs properties. ⇒ At threshold ( β → 0) dependence on β is linear. By contrast, for the axial-vector, the cross-section is [helicity amplitudes] ⇒ At threshold ( β → 0) have β3 rise. This is reflected for almost all spin choices: normality For even normality, only spin 0 and spin 2 give ΓH ∼ β O(1) is caused by gµ β1 gν β2 term in coupling. (I will come back to this.) For odd normality, only spin 1 shows Γ ∼ β The time only 1 + has a linear dependence. Higher spins ( ≥ 3) always show a steeper dependence on β Even normality: Odd normality: So, an observation of a β dependence near threshold rules allows only 0 +, 1 - or 2 + If we set the dangerous terms to zero , and (Even normality only) dependence dependence dependence Ruling out the dangerous terms: If we see or then 1 - (in fact any odd spin) is ruled out generally by Yang’s theorem Alternatively use angular correlations of the leptons SM has By contrast 0 - has so no term And the offending spin-2 term causes all so contains terms such as which are absent in the SM. 3. CP Quantum Numbers You may have noticed in the above that we also had 0 -, so we can use the same ideas to check the CP of the Higgs. A CP odd term must take the form which leads to SM here included ΓZ for both Z’s CP odd Alternatively (or above the ZZ threshold), one can use angular distributions again. This provides a very clear distinction between 0 + and 0 - states. Standard Model CP odd 4. CP violating Higgs couplings The most general vertex for a spinless particle coupling to a Z boson is SM coupling (CP even) CP even CP odd The SM is given by a=1, b=c=0. a can always be chosen to be real, but b and c can be complex. Note that and simultaneously CP violation But or CP is conserved since it may just be that the Z couples to the CP even or CP odd part A note on gauge invariance This vertex manifestly doesn’t satisfy the expected Ward identities: i.e . and In principle, one could make the extra terms in the vertex satisfy these identities by rewriting them as, for example Notice that this term still breaks the Ward identities, but this is not surprising since the Ward identities are broken also for the SM. This is because electroweak symmetry is already broken. The Ward identities only need to hold in the limit The above vertex is equivalent to the original vertex with a redefinition of a and b since extra terms like will vanish when contracted with conserved currents. The total rate The most obvious expectation is to have a SM like coupling plus an extra CP violating part, i.e and c small This will boost (or shrink) the total rate for Can we distinguish the extra couplings via that total width to Z’s? m m 1 and 2 are the virtualities of the Z-bosons, which must be integrated over Examine the total number of events observed in leptons as according to the ATLAS TDR study [Hohlfeld, ATL-PHYS-2001-004] . Initial cuts: Two leptons with Two additional leptons with All four leptons with rapidity Compare signal with background in a small window around mH and usual lepton identification and reconstruction efficiency applied. Additionally: For mH = 150 GeV, + impact parameter and isolation cuts For mH = 200 GeV, + pT of hardest Z Notice that there were no K factors in the ATLAS study. For the production this may enhance the rate by up to a factor 2 For the decay, NLO changes the rate by about 5% The ATLAS study found: For and signal: 67.6 events background: 8.92 events For and signal: 54 events background: 7 events The number of signal events will be increased or decreased by our altered coupling, but the backgrounds will stay the same. We assumed that the effect of the cuts on the signal is the same as the SM. We only allowed the HZZ coupling to change. In principle, the same physics that changes the HZZ coupling may change the HWW coupling. Although this wouldn’t effect the HZZ width, it would effect the HZZ branching ratio. Set b=0 for simplicity Scale up to SM NS is the number of signal events in the SM, and we calculated the number with an altered coupling N S. If the number of background events is N B, then we expect a typical fluctuation of the SM total events to be Then the significance of any deviation is Deviation from the SM (with b=0) 3-5 >5 σ σ <3 σ It is impossible to tell whether the difference arises from an overall factor (e.g. bigger a) or a new term in the coupling. So the total rate is not a lot of use. Also, we can’t measure the phase of c. Threshold behaviour Previously we saw how the threshold behaviour could distinguish a CP even and CP odd state. Can we do the same with a CP-violating vertex? Only one term (the square of the CP-even part) has a linear dependence on β (this comes from the phase space) However, this term will dominate the threshold dependence as long as .
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